A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also includes the prior model information. In reality, however, the true model generating the data is either unknown or simplified when deriving estimators, which motivates the works to derive estimation bounds under modeling mismatch situations. This paper provides a derivation of a Bayesian Cram\'{e}r-Rao bound under model misspecification, defining important concepts such as pseudotrue parameter that were not clearly identified in previous works. The general result is particularized in linear and Gaussian problems, where closed-forms are available and results are used to validate the results.

翻译：下限是预测某个统计模式下估计者能够达到的性能的一个重要工具。 贝叶斯界是这种界限,不仅利用观测统计,而且还包括先前的模型信息。 然而,在现实中,产生数据的真正模型在产生估计者时不是未知就是简化,这促使有关工程在模型不匹配情况下得出估计界限。 本文根据模型错误区分,提供了一种Bayesian Cram\ {e}r-Rao的产物,界定了重要概念,如以前工作中未明确查明的伪真参数。一般结果具体表现为线性问题和高斯问题,在那里有封闭形式,结果被用来验证结果。</s>